Cores of relaxed galaxy clusters are often disturbed by AGN activity as revealed by deep Chandra observations. Such perturbations reflect density and temperature fluctuations in the hot X-ray gas induced by shocks, subsonic gas motions, bubbles of relativistic plasma, etc. In my talk I will address the questions on the nature and energetics of the AGN-driven perturbations in the brightest nearby galaxy clusters, which were deeply observed by Chandra. I will present turbulence measurements and show that the heating rate due to dissipation of turbulence is sufficient to balance the radiative cooling locally at each radius within the cores, suggesting that turbulence might be the key element in resolving the gas cooling problem in cluster cores and other X-ray gas-rich systems. The results are based on the auto- and cross-spectra analysis of emissivity fluctuations in soft and hard X-ray bands over a broad range of spatial scales, down to microphysical scales.